What is the length of segment ae?
(3 points – 1 point correct formula(s), 1 point correct proportion(s), 1 point accurate calculations)

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Step-by-step explanation:

Step 1: Show that triangle ABC is similar to triangle CDE.

Segment BC is parallel to segment DE. As a result,

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Point A, C, and E lines up on segment AE. As a result, .

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As seen above, . Therefore,

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The three angles of triangle ABC adds up to . That is:

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for being a right angle. As a result,

Two of triangle ABC and CDE's angles are the same, implying that the third angle is also the same. As a result, the two triangles are similar.

Step 2: Find the ratios between the segments.

Only the length of CD is known among all three sides in triangle CDE. Side CE is part of segment AE; the length of side CE needs to be determined. Side CD corresponds to side AB, whereas side CE corresponds to side AC.

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Step 3: Find the length of AC, CE, and hence AE.

Apply the Pythagorean Theorem:

Apply the ratio found in step 2:

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